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A prism with a base area of 5 ft² and a height of 10 ft is dilated by a factor of 6/5 .



What is the volume of the dilated prism?

Enter your answer, as a decimal, in the box.

Respuesta :

IsrarAwan
First we need to find the volume of the prism without the dilated factor:

The volume would be:
Volume of the prism(without dilated) = (area of the base) * (height)
Since,
Area of base = 5[tex]ft^{2}[/tex]
Height of the prism = 10f

Volume(without dilated) = 5*10 = 50[tex]ft^{3}[/tex]

Now let us apply the dilated factor! For that you need to multiply for factor with the volume of the prism without dilation.

Volume of the dilated prism = [tex]d^{3}[/tex] * (Volume of the prism without dilation)

Where d = dilated factor. Therefore,

[tex]v = (\frac{6}{5} )^{3} * 50[/tex]


v = 86.4[tex]ft^{3}[/tex]

So the correct answer: 86.4[tex]ft^{3}[/tex]


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